breakdown point

(noun)

the number or proportion of arbitrarily large or small extreme values that must be introduced into a batch or sample to cause the estimator to yield an arbitrarily large result

Related Terms

Examples of breakdown point in the following topics:

  • Interquartile Range

    • Unlike (total) range, the interquartile range has a breakdown point of 25%.
    • All outliers are displayed as regular points on the graph.

  • Which Average: Mean, Mode, or Median?

    • The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data is contaminated, the median will not give an arbitrarily large result.
    • For example, a distribution of points in the plane will typically have a mean and a mode, but the concept of median does not apply.

  • Line fitting, residuals, and correlation exercises

    • The scatterplot on the left displays the relationship between height and fastest speed, and the scatterplot on the right displays the breakdown by gender in this relationship.
    • There will also be many points on the right above the line.
    • However, there do appear to be some anomalous observations along the left where several students have the same height that is notably far from the cloud of the other points.
    • Additionally, there are many students who appear not to have driven a car, and they are represented by a set of points along the bottom of the scatterplot.
    • We can plot these points to see they fall on a straight line, and they always will.

  • Introduction to testing for independence in two-way tables (special topic)

  • Observations, variables, and data matrices

  • Non-normal point estimates

    • We may apply the ideas of confidence intervals and hypothesis testing to cases where the point estimate or test statistic is not necessarily normal.
    • The point estimate tends towards some distribution that is not the normal distribution.
    • For each case where the normal approximation is not valid, our first task is always to understand and characterize the sampling distribution of the point estimate or test statistic.

  • Summary of Formulas

    • ( lower value,upper value ) = ( point estimate − error bound,point estimate + error bound )
    • error bound = upper value − point estimate OR error bound = (upper value − lower value)/2

  • Basic properties of point estimates

    • First, we determined that point estimates from a sample may be used to estimate population parameters.
    • We also determined that these point estimates are not exact: they vary from one sample to another.

  • Introduction to confidence intervals

    • A point estimate provides a single plausible value for a parameter.
    • However, a point estimate is rarely perfect; usually there is some error in the estimate.
    • Instead of supplying just a point estimate of a parameter, a next logical step would be to provide a plausible range of values for the parameter.
    • In Section 4.5, we generalize these methods for a variety of point estimates and population parameters that we will encounter in Chapter 5 and beyond.
    • This video introduces confidence intervals for point estimates, which are intervals that describe a plausible range for a population parameter.

  • Statistical Power

    • Discuss statistical power as it relates to significance testing and breakdown the factors that influence it.